A system using multiple tone signalling generally uses the Fourier Transform and its inverse to convert the information between time and frequency domains. Two examples of this type of modulation scheme are: (a) DMT (Discrete Multi-Tone) as used in systems such as ADSL (Asymmetric Digital Subscriber Loop); and (b) COFDM (Carrierless Orthogonal Frequency Division Multiplex), a standard widely adopted for digital terrestrial TV broadcasting.
In these systems, the data to be transmitted are sub-divided (multiplexed) across a number of distinct frequencies (sometimes also referred to as tones or sub-carriers) which are all integer multiples of a fixed basic frequency. The individual tones making up the group are spaced apart by this basic frequency. (In the case of COFDM the group of tones is then shifted up to a much higher frequency range for transmission from an aerial, but that detail is not relevant to the discussion here.) The number of tones used in different systems and within an individual system can vary, anywhere from 10 or so; e.g. for a low bandwidth ADSL upstream link, up to several thousand, e.g. an “8K-carrier” COFDM digital TV transmission.
The key algorithm common to the communication systems under consideration is the Fourier Transform, a mathematical scheme in which a time-varying signal is represented not as a set of values in time but as the sum of a set of sinusoidal waveforms. Each sinusoid in the set has a distinct frequency which is an integer multiple of a base frequency called the analysis frequency. Fourier Transform theory shows that any varying signal can be alternately represented in this way, by defining the unique set of amplitude and phase values for the individual sinusoids which sum together to form the signal wave-shape.
In the general (continuous) case, the size of the set of sinusoids is infinite and the spacing of the individual frequencies is infinitesimal. However the particular type of Fourier Transform used in practical communications systems is the Discrete Fourier Transform (DFT). The term ‘discrete’ is used because the data is processed as a set of distinct samples, not a continuous signal. When a finite sequence of samples is transformed in this way, the size of the set of sinusoids that represent the signal in the frequency domain is also finite. Hereafter, when the Fourier Transform is mentioned, the term ‘discrete’ should be assumed.
In summary, the normal (“forward”) Fourier Transform is used to convert from a series of samples taken in the time domain into an equivalent representation of the same information, namely as a series of values in the frequency domain, describing the amplitude and phase of each of a set of harmonically related sinusoidal waveforms. The reverse process, the Inverse Fourier Transform, performs the opposite operation, summing the waveforms described by the individual amplitude and phase values to re-create a composite waveform as a series of samples in the time domain.
The Fourier Transform and its inverse are relatively complex functions, but they may be implemented without difficulty using well-known algorithms on a digital signal processor. In particular, highly efficient versions of the transforms are known, commonly called the Fast Fourier Transform (FFT) and the Inverse FFT or IFFT, which operate on sample sequences whose lengths are powers of 2, e.g. 256 points or 512 points.
The FFT and IFFT together provide for efficient encoding and decoding of signals. In a transmitter, a set of data bits may be encoded by the IFFT, choosing particular combinations of amplitude and phase for each of the constituent frequency components to represent different data values. After all the data is encoded into the amplitude and phase of each constituent tone, the IFFT is performed to create a time-domain signal which is then transmitted.
For example, it is possible to encode 2 bits of data, representing 4 different possible values (00, 01, 10, 11), on to one tone by simple quadrature modulation, where the amplitude is held constant and four distinct phase values (e.g. +45, +135, +225, +315 degrees, i.e. 90 degrees apart) represent the 4 different combinations. More complex mappings are possible (allowing more bits to be encoded on one tone) using more phase values, or combinations of different amplitudes as well as phases. In practical systems, modulation of one tone can be varied so as to represent as many as 15 or 16 bits in the best case (using 32768 or 65536 distinct combinations of amplitude and phase). Therefore in systems using hundreds of tones, some thousands of bits can be carried in each symbol in good circumstances.
The (forward) FFT is used at the receiver to reverse the process. Once time synchronization with the transmitted waveform has been achieved and equalisation for frequency-dependent phase and amplitude changes (inevitable in the transfer of the signal from transmitter to receiver) has been performed, the FFT is applied to the set of samples making up each received symbol, to reconstruct values of amplitude and phase for each of the tones in use. In general the values obtained by this process are not exactly the same as were initially encoded, for various reasons, including particularly the presence of noise introduced along the transmission path of the signal. Noise is unavoidable in any practical system. However, by applying various techniques to compensate for errors caused by noise, the original data may be recovered with an acceptable level of reliability, provided the system has been configured appropriately, taking into account the signal-transfer characteristics of the transmission path.
In order to ease the work of the receiver in equalizing the received signal for the effects of the transmission route, it is common to insert a short delay between consecutive symbols transmitted. In ADSL, this delay period is called the “cyclic prefix time”, in which what is transmitted is a portion of the signal extracted from the end of the immediately following symbol. The name “cyclic prefix” time derives from the fact that the short sequence has been used as a prefix to the new symbol and is cyclically congruent with it. Note that after equalization, the signal received during the cyclic prefix time is ignored by the receiver. In COFDM, the delay period is called the “guard time”; no signal is transmitted during this time.
The IFFT-FFT (encoding-decoding) process provides for great flexibility in the communications system. Different frequencies in the spectrum covered by the set of tones may have different characteristics in respect of noisiness and attenuation over the communication link (e.g. the phone line in the case of an ADSL system). By varying the encoding details tone by tone, this may be accounted for, so as to maximize the number of bits carried by the symbol in total, even when a particular single tone can only carry a small number of bits. U.S. Pat. No. 4,679,227, which describes multi-tone encoding schemes, presents techniques for accomplishing this.
One property of this type of signal encoding is particularly relevant. The waveform resulting from the IFFT can in principle have very large peak values in it—relative to the average amplitude of the signal as a whole—at points where the particular phases of the individual tones happen to sum together in the same direction. For example, if all tones were using encoded simple 2-bit quadrature modulation, and all the data bits being modulated were zero (or more generally if the same pair of bit values were modulating each tone), then at the start of the time domain symbol created by the IFFT there would be a high amplitude “spike”, since each component waveform would have a real positive value 0.707 times its peak amplitude, and these would all sum together in the same direction. By contrast, if there is a general haphazard distribution of 1's and 0's in the data, the expected peak value in the average symbol would be much lower, although once in a while peaks will still occur.
On observing the output from a sequence of IFFT operations used to encode a (generalised) data sequence for transmission, the signal is seen to have a sample amplitude distribution which is very like random noise, when considered on a statistical basis. The most frequently occurring sample amplitudes are those near zero (the central point—the distribution is symmetrical either side of zero). Higher amplitudes are less likely, but still occur, and there is a gradual reduction in likelihood of occurrence with increasing amplitude. The very highest sample amplitudes which can occur—unlike with true noise there is a finite limit because we use a discrete IFFT over a finite number of tones—are still many times higher than the average signal amplitude; however, such values occur only extremely infrequently.
The overall statistical properties of the sequence are complex. However, one simple measure of the properties of signals generally is their crest factor. The crest factor of a repetitive signal is defined as the ratio of its peak amplitude to its average (RMS) amplitude. Different types of waveforms can have very different crest factors, depending on their shape. For example a simple pulse waveform, where the signal jumps between just two levels +A and −A, has a crest factor of 1, i.e. the average and peak levels of the signal are the same. A simple continuous sine wave has a crest factor of √2 (1.4142135 . . . ). Other wave shapes can be envisaged having widely differing crest factors.
When we are dealing with irregular (non-repeating) signals, such as the output from an IFFT process applied to a random stream of data, the definition of crest factor is adjusted. This is necessary, in order to take into account the statistical spread of amplitude values. In such cases we define the effective crest factor to be the ratio of a threshold level to the average (RMS) level of the signal overall, where the threshold level is that which only some particular small fraction (e.g. 1/10,000,000th, or 10−7) of the generated samples will equal or exceed.
With signals created by an IFFT-based modulator, in general, systems in which few tones are used will have a smaller effective crest factor than systems with large numbers of tones. In a typical ADSL system, using 220 tones on the downstream path, the effective crest factor is around 5.3 at the 10−7 probability threshold.
In practical systems based on the IFFT/FFT pairing, various steps are taken to reduce the impact of its sensitivity to regular patterns of input data. These can readily occur in data sequences delivered to an encoder, especially in the case of ADSL where a fixed padding data pattern must be inserted when no user data is waiting to be transmitted. The problem of such regular patterns in the original data causing high peaks in the output of the IFFT is usually dealt with by performing a reversible “scrambling” operation on the data stream prior to encoding. Two examples of such scrambling mechanisms are self-scramblers and randomisers.
By applying scrambling processes to the input data, any regular patterns in it may be broken up. The distribution of the data bit values going forward into the encoder becomes more haphazard, and so the likelihood of coherence between the phases of the different tones is drastically reduced. This diminishes the frequency with which spikes appear in the time-domain signal, even for a completely regular input stream (e.g. all 1s), relative to that which would apply without scrambling. However, for more irregular input data, no particular change in the statistical properties of the IFFT output will occur.
One major problem with IFFT-based encoding, so far as the design of any practical system is concerned, is that the time domain signal created has characteristics which make it more difficult and/or more expensive to carry through the later stages of the transmission path. For example, the bandwidth of the signal may in some cases be as wide as can theoretically be carried by the discrete sample sequence. Any subsequent processing of the signal, post-IFFT, must therefore be carefully designed to minimise distortions of the signal caused by frequency-dependent variations (e.g. in gain or phase-shift), which are typically worst at the highest frequencies.
However, an issue of great concern is the high crest factor of a typical IFFT-generated signal. This leads to a number of difficulties in designing the circuitry in a modulator & transmitter for an IFFT-based modulation scheme. Some of the problems also occur in the design of a corresponding multi-tone receiving device.
The first problem is that the dynamic range of the digital-to-analogue converter (DAC) must be large, requiring a relatively high number of bits of resolution (typically between 14 and 16 for ADSL). This makes the DAC hard to design, especially since it is running at high sampling rates (in the order of 1–2 MHz or higher for ADSL, and higher still for COFDM). In a receiver for the transmitted signal, the input circuitry must also have a high dynamic range and low noise and distortion; equally its analogue-to-digital converter must have high linearity and resolution.
The second aspect, which is usually considered even more serious, is that it is extremely difficult to design the amplification stages of the transmitter to both yield the high linearity which is needed and also maintain good power efficiency. Because the amplifier (also called the “line-driver” in the case of ADSL) must be able to handle signal peaks several times higher than the average signal level on the line, it becomes necessary to run its power supply at a far higher voltage than the average signal level would require, if the signal's crest factor were lower. Typical power efficiencies for amplifiers in present-day ADSL system designs are therefore significantly lower than in some other types of transmission system e.g. 15–20% as against 40% or more.
Accordingly, it would be desirable to reduce the crest factor, compensate for its effects, or both.
WO99/18662 to Ericsson describes one approach to minimise effects of peaks in transmitted power in a multi-carrier DSL-type transmission system. In this arrangement, an amplifier circuit arranged for driving the line from an analogue input has two power supplies, of higher and lower voltage. A controller causes power to be supplied from the lower voltage power supply when the magnitude of the input signal is less than a threshold, and from the higher voltage power supply when the magnitude of the input signal is higher than the threshold.
Unfortunately, the signal and sampling frequencies involved in typical multi-tone transmission are very high, with sampling periods of order 50–500 nanoseconds. This period is very much less than the time it would take for a dual-supply amplifier to switch power supply voltage and resume stable operation at the new voltage. It is therefore difficult to design an amplifier of this sort in a way which avoids both transient distortions and the introduction of noise at the moment of switching supply voltages. Practical amplifier designs intended to support more power-efficient multi-tone transmission therefore do not use such a technique, precisely to avoid such noise and distortion effects, which are likely to be seriously damaging to multi-tone signals. An example of an amplifier which supports dual supply operation, without using an explicit controlled hard switch-over, is described in “THS6032 Low power ADSL central-office line driver”, (document ID SLOS233D, April 1999, revised May 2001, Texas Instruments Incorporated, Dallas Tex., USA). This design exploits “soft” or continuous transition between supply voltages (so-called “class-G Operation”) even though this results in considerably lower power efficiency than might be obtained from the “hard” (instant) switching amplifier controlled by a separate control signal, such as WO99/18662 describes.
There thus remains a need to reduce or compensate for the crest factor in multi-tone systems.